C Notes

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Bitwise Operators in C Programming

Complete guide to bitwise operators in C: AND, OR, XOR, NOT, left shift, and right shift. Learn practical applications like flag manipulation, masking, and power-of-2 operations with examples.

Bitwise operators work directly on the binary representation of numbers, manipulating individual bits. While they might seem low-level and intimidating at first, they're incredibly powerful tools used in systems programming, embedded development, networking, graphics, and cryptography. If you want to write efficient C code, mastering bitwise operators is non-negotiable.

The Six Bitwise Operators

Operator	Name	Description
`&`	Bitwise AND	Sets bit to 1 if both bits are 1
`	`	Bitwise OR	Sets bit to 1 if at least one bit is 1
`^`	Bitwise XOR	Sets bit to 1 if bits are different
`~`	Bitwise NOT	Inverts all bits (one's complement)
`<<`	Left Shift	Shifts bits to the left
`>>`	Right Shift	Shifts bits to the right

Bitwise AND (&)

The AND operator compares each bit of two numbers. The result bit is 1 only if BOTH corresponding bits are 1.

Example

5 = 0101 & 3 = 0011 ----------- 1 = 0001

c example

#include <stdio.h>

int main() {
    unsigned int a = 12;  // 1100
    unsigned int b = 10;  // 1010

    printf("12 & 10 = %u\n", a & b);  // 1000 = 8

    // Practical: Check if a number is even or odd
    int num = 7;
    if (num & 1) {
        printf("%d is odd\n", num);
    } else {
        printf("%d is even\n", num);
    }

    // Practical: Masking - extract lower 4 bits
    unsigned int value = 0xAB;  // 10101011
    unsigned int lower_nibble = value & 0x0F;  // 00001011 = 11
    printf("Lower nibble of 0xAB: %u (0x%X)\n", lower_nibble, lower_nibble);

    return 0;
}

Output

12 & 10 = 8
7 is odd
Lower nibble of 0xAB: 11 (0xB)

Bitwise OR (|)

The OR operator sets the result bit to 1 if EITHER or BOTH corresponding bits are 1.

Example

5 = 0101 | 3 = 0011 ----------- 7 = 0111

c example

#include <stdio.h>

int main() {
    unsigned int a = 12;  // 1100
    unsigned int b = 10;  // 1010

    printf("12 | 10 = %u\n", a | b);  // 1110 = 14

    // Practical: Setting flags
    unsigned int permissions = 0;
    unsigned int READ  = 1;  // 001
    unsigned int WRITE = 2;  // 010
    unsigned int EXEC  = 4;  // 100

    permissions = READ | WRITE;  // Set read and write
    printf("Permissions (R+W): %u\n", permissions);  // 011 = 3

    permissions = permissions | EXEC;  // Add execute
    printf("Permissions (R+W+X): %u\n", permissions);  // 111 = 7

    return 0;
}

Output

12 | 10 = 14
Permissions (R+W): 3
Permissions (R+W+X): 7

Bitwise XOR (^)

XOR (exclusive OR) sets the result bit to 1 only when the two bits are DIFFERENT.

Example

5 = 0101 ^ 3 = 0011 ----------- 6 = 0110

Example

#include <stdio.h> int main() { unsigned int a = 12; // 1100 unsigned int b = 10; // 1010 printf("12 ^ 10 = %u\n", a ^ b); // 0110 = 6 // Practical: Swap without temp variable int x = 25, y = 42; printf("Before: x=%d, y=%d\n", x, y); x = x ^ y; y = x ^ y; x = x ^ y; printf("After: x=%d, y=%d\n", x, y); // XOR property: a ^ a = 0, a ^ 0 = a printf("5 ^ 5 = %d\n", 5 ^ 5); printf("5 ^ 0 = %d\n", 5 ^ 0); // Practical: Find the non-duplicate number int arr[] = {2, 3, 5, 3, 2}; int result = 0; for (int i = 0; i < 5; i++) { result ^= arr[i]; } printf("Non-duplicate: %d\n", result); return 0; }

Output

12 ^ 10 = 6
Before: x=25, y=42
After:  x=42, y=25
5 ^ 5 = 0
5 ^ 0 = 5
Non-duplicate: 5

Bitwise NOT (~)

The NOT operator (one's complement) inverts every bit — 0 becomes 1 and 1 becomes 0.

c example

#include <stdio.h>

int main() {
    unsigned char a = 5;   // 00000101
    unsigned char result = ~a;  // 11111010 = 250

    printf("~5 (unsigned char) = %u\n", result);

    // With signed integers (two's complement)
    int b = 5;
    printf("~5 (signed int) = %d\n", ~b);  // -6

    // Relationship: ~n = -(n+1)
    printf("~0 = %d\n", ~0);    // -1
    printf("~1 = %d\n", ~1);    // -2
    printf("~(-1) = %d\n", ~(-1));  // 0

    return 0;
}

Output

~5 (unsigned char) = 250
~5 (signed int) = -6
~0 = -1
~1 = -2
~(-1) = 0

Key insight: For signed integers, ~n = -(n+1). This is because of two's complement representation.

Left Shift Operator (<<)

Left shift moves all bits to the left by the specified number of positions. Vacated positions on the right are filled with zeros. Each left shift effectively multiplies the number by 2.

Example

#include <stdio.h> int main() { unsigned int a = 5; // 00000101 printf("5 << 1 = %u\n", a << 1); // 00001010 = 10 printf("5 << 2 = %u\n", a << 2); // 00010100 = 20 printf("5 << 3 = %u\n", a << 3); // 00101000 = 40 // Left shift = multiply by 2^n int num = 7; printf("%d * 2 = %d (using <<)\n", num, num << 1); printf("%d * 4 = %d (using <<)\n", num, num << 2); printf("%d * 8 = %d (using <<)\n", num, num << 3); // Practical: Create bit masks for (int i = 0; i < 8; i++) { printf("1 << %d = %3d (", i, 1 << i); // Print binary for (int j = 7; j >= 0; j--) { printf("%d", ((1 << i) >> j) & 1); } printf(")\n"); } return 0; }

Output

5 << 1 = 10
5 << 2 = 20
5 << 3 = 40
7 * 2 = 14 (using <<)
7 * 4 = 28 (using <<)
7 * 8 = 56 (using <<)
1 << 0 =   1 (00000001)
1 << 1 =   2 (00000010)
1 << 2 =   4 (00000100)
1 << 3 =   8 (00001000)
1 << 4 =  16 (00010000)
1 << 5 =  32 (00100000)
1 << 6 =  64 (01000000)
1 << 7 = 128 (10000000)

Right Shift Operator (>>)

Right shift moves bits to the right. For unsigned numbers, vacated positions are filled with 0. For signed numbers, the behavior depends on the implementation (usually arithmetic shift — fills with sign bit).

c example

#include <stdio.h>

int main() {
    unsigned int a = 40;  // 00101000

    printf("40 >> 1 = %u\n", a >> 1);  // 00010100 = 20
    printf("40 >> 2 = %u\n", a >> 2);  // 00001010 = 10
    printf("40 >> 3 = %u\n", a >> 3);  // 00000101 = 5

    // Right shift = divide by 2^n (integer division)
    int num = 100;
    printf("%d / 2 = %d (using >>)\n", num, num >> 1);
    printf("%d / 4 = %d (using >>)\n", num, num >> 2);
    printf("%d / 8 = %d (using >>)\n", num, num >> 3);

    // Signed right shift (implementation-defined)
    int negative = -16;
    printf("-16 >> 1 = %d\n", negative >> 1);  // Usually -8 (arithmetic shift)

    return 0;
}

Output

40 >> 1 = 20
40 >> 2 = 10
40 >> 3 = 5
100 / 2 = 50 (using >>)
100 / 4 = 25 (using >>)
100 / 8 = 12 (using >>)
-16 >> 1 = -8

Practical Applications

Setting, Clearing, and Toggling Bits

c example

#include <stdio.h>

int main() {
    unsigned int flags = 0;

    // Set bit n: use OR with mask
    flags |= (1 << 3);  // Set bit 3
    printf("After setting bit 3: %u\n", flags);  // 8

    // Clear bit n: use AND with inverted mask
    flags = 15;  // 1111
    flags &= ~(1 << 2);  // Clear bit 2
    printf("After clearing bit 2 from 15: %u\n", flags);  // 1011 = 11

    // Toggle bit n: use XOR with mask
    flags = 10;  // 1010
    flags ^= (1 << 1);  // Toggle bit 1
    printf("After toggling bit 1 of 10: %u\n", flags);  // 1000 = 8

    // Check if bit n is set
    int value = 13;  // 1101
    int bit_pos = 2;
    if (value & (1 << bit_pos)) {
        printf("Bit %d is SET in %d\n", bit_pos, value);
    }

    return 0;
}

Output

After setting bit 3: 8
After clearing bit 2 from 15: 11
After toggling bit 1 of 10: 8
Bit 2 is SET in 13

Counting Set Bits (Brian Kernighan's Algorithm)

Example

#include <stdio.h> int countSetBits(unsigned int n) { int count = 0; while (n) { n &= (n - 1); // Clears the lowest set bit count++; } return count; } int main() { unsigned int num = 29; // 11101 -> 4 set bits printf("Number of set bits in %u: %d\n", num, countSetBits(num)); printf("Set bits in 7: %d\n", countSetBits(7)); // 111 -> 3 printf("Set bits in 16: %d\n", countSetBits(16)); // 10000 -> 1 return 0; }

Output

Number of set bits in 29: 4
Set bits in 7: 3
Set bits in 16: 1

Check if Number is Power of 2

Example

#include <stdio.h> int isPowerOfTwo(unsigned int n) { return n > 0 && (n & (n - 1)) == 0; } int main() { for (int i = 1; i <= 20; i++) { if (isPowerOfTwo(i)) { printf("%d is a power of 2\n", i); } } return 0; }

Output

1 is a power of 2
2 is a power of 2
4 is a power of 2
8 is a power of 2
16 is a power of 2

Common Bit Manipulation Tricks

Operation	Expression	Description
Check odd/even	`n & 1`	Returns 1 if odd
Multiply by 2^k	`n << k`	Faster than multiplication
Divide by 2^k	`n >> k`	Faster than division
Set bit i	`n	= (1 << i)`	Turn on specific bit
Clear bit i	`n &= ~(1 << i)`	Turn off specific bit
Toggle bit i	`n ^= (1 << i)`	Flip specific bit
Check bit i	`n & (1 << i)`	Non-zero if bit is set
Power of 2 check	`n & (n-1) == 0`	True for powers of 2
Turn off rightmost set bit	`n & (n-1)`	Kernighan's trick
Isolate rightmost set bit	`n & (-n)`	Gets lowest set bit

Interview Questions

Q1: How would you swap two numbers using XOR without a temporary variable?

c example

a = a ^ b;
b = a ^ b;  // b = (a^b)^b = a
a = a ^ b;  // a = (a^b)^a = b

This works because XOR is its own inverse: a ^ a = 0 and a ^ 0 = a. However, this fails if both variables point to the same memory location.

Q2: How can you check if a number is a power of 2 using bitwise operators?

Use n & (n - 1) == 0 (for n > 0). Powers of 2 have exactly one bit set (e.g., 8 = 1000). Subtracting 1 flips all bits below and including that bit (7 = 0111). AND-ing them gives 0 only for powers of 2.

Q3: What is the difference between >> for signed and unsigned integers?

For unsigned integers, right shift always fills with 0 (logical shift). For signed integers, the behavior is implementation-defined — most compilers use arithmetic shift (fills with the sign bit), so negative numbers remain negative after right shift.

Q4: How do you count the number of set bits in an integer efficiently?

Brian Kernighan's algorithm: repeatedly do n = n & (n-1) which clears the lowest set bit each time. Count iterations until n becomes 0. This runs in O(number of set bits) time, which is optimal.

Q5: What's the difference between ~ and ! in C?

~ is bitwise NOT — it inverts every bit of the number (~5 = -6 for signed int). ! is logical NOT — it returns 1 if the operand is 0, and 0 for any non-zero value (!5 = 0). They serve completely different purposes.

Summary

Bitwise operators work on individual bits: &, |, ^, ~, <<, >>
Left shift multiplies by powers of 2; right shift divides by powers of 2
AND is used for masking and clearing bits; OR is used for setting bits
XOR is useful for toggling and has the property that a ^ a = 0
n & (n-1) clears the lowest set bit — the basis for many bit tricks
Always use unsigned types for predictable bitwise behavior
Bit manipulation is crucial for embedded systems, networking, and performance-critical code

Exam Focus

Revise definitions, diagrams, examples, and short-answer points for Bitwise Operators in C Programming.

Interview Use

Prepare one clear explanation, one practical example, and one common mistake for this C Programming topic.

Search Terms

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Continue learning this concept

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C Notes

Bitwise Operators in C Programming

Complete guide to bitwise operators in C: AND, OR, XOR, NOT, left shift, and right shift. Learn practical applications like flag manipulation, masking, and power-of-2 operations with examples.

The Six Bitwise Operators

Operator	Name	Description
`&`	Bitwise AND	Sets bit to 1 if both bits are 1
`	`	Bitwise OR	Sets bit to 1 if at least one bit is 1
`^`	Bitwise XOR	Sets bit to 1 if bits are different
`~`	Bitwise NOT	Inverts all bits (one's complement)
`<<`	Left Shift	Shifts bits to the left
`>>`	Right Shift	Shifts bits to the right

Bitwise AND (&)

The AND operator compares each bit of two numbers. The result bit is 1 only if BOTH corresponding bits are 1.

Example

5 = 0101 & 3 = 0011 ----------- 1 = 0001

c example

#include <stdio.h>

int main() {
    unsigned int a = 12;  // 1100
    unsigned int b = 10;  // 1010

    printf("12 & 10 = %u\n", a & b);  // 1000 = 8

    // Practical: Check if a number is even or odd
    int num = 7;
    if (num & 1) {
        printf("%d is odd\n", num);
    } else {
        printf("%d is even\n", num);
    }

    // Practical: Masking - extract lower 4 bits
    unsigned int value = 0xAB;  // 10101011
    unsigned int lower_nibble = value & 0x0F;  // 00001011 = 11
    printf("Lower nibble of 0xAB: %u (0x%X)\n", lower_nibble, lower_nibble);

    return 0;
}

Output

12 & 10 = 8
7 is odd
Lower nibble of 0xAB: 11 (0xB)

Bitwise OR (|)

The OR operator sets the result bit to 1 if EITHER or BOTH corresponding bits are 1.

Example

5 = 0101 | 3 = 0011 ----------- 7 = 0111

c example

#include <stdio.h>

int main() {
    unsigned int a = 12;  // 1100
    unsigned int b = 10;  // 1010

    printf("12 | 10 = %u\n", a | b);  // 1110 = 14

    // Practical: Setting flags
    unsigned int permissions = 0;
    unsigned int READ  = 1;  // 001
    unsigned int WRITE = 2;  // 010
    unsigned int EXEC  = 4;  // 100

    permissions = READ | WRITE;  // Set read and write
    printf("Permissions (R+W): %u\n", permissions);  // 011 = 3

    permissions = permissions | EXEC;  // Add execute
    printf("Permissions (R+W+X): %u\n", permissions);  // 111 = 7

    return 0;
}

Output

12 | 10 = 14
Permissions (R+W): 3
Permissions (R+W+X): 7

Bitwise XOR (^)

XOR (exclusive OR) sets the result bit to 1 only when the two bits are DIFFERENT.

Example

5 = 0101 ^ 3 = 0011 ----------- 6 = 0110

Example

Output

12 ^ 10 = 6
Before: x=25, y=42
After:  x=42, y=25
5 ^ 5 = 0
5 ^ 0 = 5
Non-duplicate: 5

Bitwise NOT (~)

The NOT operator (one's complement) inverts every bit — 0 becomes 1 and 1 becomes 0.

c example

#include <stdio.h>

int main() {
    unsigned char a = 5;   // 00000101
    unsigned char result = ~a;  // 11111010 = 250

    printf("~5 (unsigned char) = %u\n", result);

    // With signed integers (two's complement)
    int b = 5;
    printf("~5 (signed int) = %d\n", ~b);  // -6

    // Relationship: ~n = -(n+1)
    printf("~0 = %d\n", ~0);    // -1
    printf("~1 = %d\n", ~1);    // -2
    printf("~(-1) = %d\n", ~(-1));  // 0

    return 0;
}

Output

~5 (unsigned char) = 250
~5 (signed int) = -6
~0 = -1
~1 = -2
~(-1) = 0

Key insight: For signed integers, ~n = -(n+1). This is because of two's complement representation.

Left Shift Operator (<<)

Left shift moves all bits to the left by the specified number of positions. Vacated positions on the right are filled with zeros. Each left shift effectively multiplies the number by 2.

Example

Output

5 << 1 = 10
5 << 2 = 20
5 << 3 = 40
7 * 2 = 14 (using <<)
7 * 4 = 28 (using <<)
7 * 8 = 56 (using <<)
1 << 0 =   1 (00000001)
1 << 1 =   2 (00000010)
1 << 2 =   4 (00000100)
1 << 3 =   8 (00001000)
1 << 4 =  16 (00010000)
1 << 5 =  32 (00100000)
1 << 6 =  64 (01000000)
1 << 7 = 128 (10000000)

Right Shift Operator (>>)

c example

#include <stdio.h>

int main() {
    unsigned int a = 40;  // 00101000

    printf("40 >> 1 = %u\n", a >> 1);  // 00010100 = 20
    printf("40 >> 2 = %u\n", a >> 2);  // 00001010 = 10
    printf("40 >> 3 = %u\n", a >> 3);  // 00000101 = 5

    // Right shift = divide by 2^n (integer division)
    int num = 100;
    printf("%d / 2 = %d (using >>)\n", num, num >> 1);
    printf("%d / 4 = %d (using >>)\n", num, num >> 2);
    printf("%d / 8 = %d (using >>)\n", num, num >> 3);

    // Signed right shift (implementation-defined)
    int negative = -16;
    printf("-16 >> 1 = %d\n", negative >> 1);  // Usually -8 (arithmetic shift)

    return 0;
}

Output

40 >> 1 = 20
40 >> 2 = 10
40 >> 3 = 5
100 / 2 = 50 (using >>)
100 / 4 = 25 (using >>)
100 / 8 = 12 (using >>)
-16 >> 1 = -8

Practical Applications

Setting, Clearing, and Toggling Bits

c example

#include <stdio.h>

int main() {
    unsigned int flags = 0;

    // Set bit n: use OR with mask
    flags |= (1 << 3);  // Set bit 3
    printf("After setting bit 3: %u\n", flags);  // 8

    // Clear bit n: use AND with inverted mask
    flags = 15;  // 1111
    flags &= ~(1 << 2);  // Clear bit 2
    printf("After clearing bit 2 from 15: %u\n", flags);  // 1011 = 11

    // Toggle bit n: use XOR with mask
    flags = 10;  // 1010
    flags ^= (1 << 1);  // Toggle bit 1
    printf("After toggling bit 1 of 10: %u\n", flags);  // 1000 = 8

    // Check if bit n is set
    int value = 13;  // 1101
    int bit_pos = 2;
    if (value & (1 << bit_pos)) {
        printf("Bit %d is SET in %d\n", bit_pos, value);
    }

    return 0;
}

Output

After setting bit 3: 8
After clearing bit 2 from 15: 11
After toggling bit 1 of 10: 8
Bit 2 is SET in 13

Counting Set Bits (Brian Kernighan's Algorithm)

Example

Output

Number of set bits in 29: 4
Set bits in 7: 3
Set bits in 16: 1

Check if Number is Power of 2

Example

Output

1 is a power of 2
2 is a power of 2
4 is a power of 2
8 is a power of 2
16 is a power of 2

Common Bit Manipulation Tricks

Operation	Expression	Description
Check odd/even	`n & 1`	Returns 1 if odd
Multiply by 2^k	`n << k`	Faster than multiplication
Divide by 2^k	`n >> k`	Faster than division
Set bit i	`n	= (1 << i)`	Turn on specific bit
Clear bit i	`n &= ~(1 << i)`	Turn off specific bit
Toggle bit i	`n ^= (1 << i)`	Flip specific bit
Check bit i	`n & (1 << i)`	Non-zero if bit is set
Power of 2 check	`n & (n-1) == 0`	True for powers of 2
Turn off rightmost set bit	`n & (n-1)`	Kernighan's trick
Isolate rightmost set bit	`n & (-n)`	Gets lowest set bit

Interview Questions

Q1: How would you swap two numbers using XOR without a temporary variable?

c example

a = a ^ b;
b = a ^ b;  // b = (a^b)^b = a
a = a ^ b;  // a = (a^b)^a = b

This works because XOR is its own inverse: a ^ a = 0 and a ^ 0 = a. However, this fails if both variables point to the same memory location.

Q2: How can you check if a number is a power of 2 using bitwise operators?

Q3: What is the difference between >> for signed and unsigned integers?

Q4: How do you count the number of set bits in an integer efficiently?

Brian Kernighan's algorithm: repeatedly do n = n & (n-1) which clears the lowest set bit each time. Count iterations until n becomes 0. This runs in O(number of set bits) time, which is optimal.

Q5: What's the difference between ~ and ! in C?

Summary

Bitwise operators work on individual bits: &, |, ^, ~, <<, >>
Left shift multiplies by powers of 2; right shift divides by powers of 2
AND is used for masking and clearing bits; OR is used for setting bits
XOR is useful for toggling and has the property that a ^ a = 0
n & (n-1) clears the lowest set bit — the basis for many bit tricks
Always use unsigned types for predictable bitwise behavior
Bit manipulation is crucial for embedded systems, networking, and performance-critical code

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Revise definitions, diagrams, examples, and short-answer points for Bitwise Operators in C Programming.

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Prepare one clear explanation, one practical example, and one common mistake for this C Programming topic.

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